As a traditional AP user I like to get the Doran's ring first, just cause. Since I never really charge in at first, I take the time to build the Nashor's Tooth because it gives great Attack Speed, AP, and Cooldown Reduction. After I get the tooth, I start building the Sorcerer's shoes for the Magic penetration to maximize the damage. Then i build the Malady because I really like to focus on her basic attacks. Her passive deals a lot of damage and the Malady adds magic damage to every hit and it also drains the enemies Magic resist. After that I get Rabadon's Deathcap for the obvious reason ;). Then i get the Rylai's for the extra tankyness and that slow is pretty nice.

Early game this skill build is great. Make sure you partner up though, but use crescent strike to wear down the enemy's hp. Then hide in the bushes, wait for the enemy to push then use crescent strike to break the ice. When they start to run back to their turret, use moon fall to draw one, or both of them, in and just focus on them. If the one your targeting is starting to get away, use Crescent strike again.

The runes I have work of me, but if you have any suggestions feel free to let me know =).
But I the quint of intellect because I use more mana with Diana than anyone else, especially when chasing, which is also why i have mana regen runes. She also works good with a little defense, I also have a few cooldown glyphs as well (-0.65 x2).

I use heal because I don't like having less than half hp and i also don't like to recall too much and it helps my laning partner.
I also use Teleport because it allows me to gank other lanes if I am too far away or if I need to get back to my turret if it's being attacked or even just getting back to my lane to help push.